1. Field of the Invention
This invention relates to a single crystal gallium nitride (GaN) substrate for producing blue light emitting diodes (LEDs) and blue light laser diodes (LDs) composed of group 3-5 nitride type semiconductors, a method of growing a single crystal gallium nitride substrate, and a method of producing a single crystal gallium nitride substrate.
This application claims the priority of Japanese Patent Applications No.2001-284323 filed on Sep. 19, 2001 and No.2002-230925 filed on Aug. 8, 2002, which are incorporated herein by reference.
Blue light emitting diodes (LEDs) based upon the group 3-5 nitride type semiconductors (InGaN, GaN) have been manufactured, sold and used on a large scale. Almost all the practical nitride type LEDs are made upon insulating sapphire (.alpha.−Al.sub.2O.sub.3) substrates. Sapphire belongs to trigonal symmetry group (a=b=c, .alpha., .beta., .gamma.<120, .noteq.90). GaN films and InGaN films are heteroepitaxially grown on a sapphire three rotationally symmetric plane for producing LEDs. On-SiC GaN type LEDs having a silicon carbide SiC substrate have been proposed and used on a small scale. On-sapphire LEDs made upon sapphire substrates have very high dislocation density of 10.sup.9 to 10.sup.10 cm.sup.−2. Despite great many dislocations, on-sapphire LEDs do not degenerate and enjoy a long lifetime.
Since low-cost techniques of manufacturing sapphire have been established, sapphire substrates are easily produced and are sales on the market at an inexpensive price.
Sapphire is chemically stable, physically sturdy and rigid. Sapphire crystal plates have been most suitable for substrates of blue light emitting device chips. Sapphire will be favorably used as a substrate for making blue light LEDs and LDs in future.
Sapphire has, however, some drawbacks as a substrate. Sapphire lacks natural cleavage. Sapphire is an insulator. Lack of natural cleavage incurs a problem of chip-division. A device-fabricated sapphire wafer is cut and separated into individual device chips by mechanical dicing. The mechanical dicing lowers the yield and enhances the cost.
Insulating sapphire cannot lead electric current. A sapphire substrate cannot be an n-type substrate which carries an n-electrode at the bottom as a cathode. Then, InGaN-type LEDs are made by piling a thick n-GaN film on the insulating sapphire substrate, epitaxially growing n-GaN, n-InGaAs, p-GaN films, etching away a peripheral part of the epitaxial films from the top p-GaN film to the lowest n-GaN film, forming an n-electrode upon an exposed region of the n-GaN film, and forming a p-electrode on the top p-GaN film. Thus, on-sapphire devices must have a wide double-stepped shape. The intermediate n-GaN requires an extra area of a chip. Twice wirebondings are required for connecting n- and p-electrodes formed on upper layers with two lead pins. Extra etching and extra wirebonding increase steps and time of fabrication. The upper n-electrode curtails an effective area of a light emitting region. The extra area and the extra steps enhance the cost.
The above is drawbacks of sapphire as a substrate of an LED. Additional weak points appear as a substrate of an LD (laser diode). An LD requires a set of resonator mirrors for reflecting light reciprocally and amplifying light power by repetition of stimulation. Sapphire lacks cleavage. Resonator mirrors cannot be fabricated on on-sapphire LDs by cleavage. The resonator mirrors should be formed by mechanical polishing or etching which requires much time. The further weak point of the on-sapphire LDs is extremely high dislocation density. GaN, InGaN or AlGaN films grown on sapphire substrates have many dislocations of more than 10.sup.9 cm.sup.−2. Despite high density of dislocations, InGaN LEDs emanate blue, green light with high efficiency and a long lifetime. But in the case of InGaN-laser diodes (LDs), excess high density of current flowing at a narrow area will degenerate LDs. Sapphire substrates have been the most prevalent substrates for InGaN LEDs till now. Sapphire, however, will not necessarily the most suitable substrates for InGaN-LDs in future.
2. Description of Related Art
The most suitable substrate for nitride type (InGaN) LDs and LEDs should be a GaN single crystal substrate which allows InGaN, GaN, AlGaN films to grow homoepitaxially. But, immaturity of crystal growth technology forbids device makers from obtaining wide, high quality GaN single crystal wafers till now. If high quality, wide GaN single crystal wafers can be manufactured, GaN single crystal wafers will be the optimum substrates for the nitride type LDs. GaN has advantages over sapphire. First of all, GaN has natural cleavage. Cleavability facilitates wafer-to-chip separation and enhances yield of the process. Resonator mirrors can be formed by the natural cleavage. An n-type GaN substrate has electric conductivity. The n-GaN substrate allows an LD or an LED to have an n-electrode at the bottom of a chip. The bottom n-electrode simplifies the device structure and widens the area of a light emanating region. There is no lattice misfit between the substrate and epi-films, which reduces the possibility of incurring inner stress and distortion. The lattice fitting will ensure a long lifetime for nitride type LDs.
However, it is impossible to make a melt of gallium nitride (GaN), since heating does not convert GaN polycrystals into a melt but sublimes GaN polycrystals into vapor. Thus, Czochralski method and Bridgman method which a melt polycrystal material into a melt, cool a part of the melt and make a large single crystal bulk solid at a thermal equilibrium, are unavailable for making a GaN single crystal. Somebody says that it may be possible to make a single crystal GaN bulk by heating under ultrahigh-pressure which forbids GaN from subliming. But, the allegation has not been confirmed. Even the ultrahigh-pressure would make a GaN melt, very small GaN crystals would be made by the melt of GaN. Such tiny crystal is no use for making a large diameter wafer of GaN.
A new method of making a thick GaN film on a foreign material substrate (e.g., sapphire) by vapor phase epitaxial growth method was proposed. It is an extension of a film growth method. However, a sapphire substrate which is chemically stable and physically rigid cannot be eliminated after the GaN film has been grown on the sapphire substrate. Thus, sapphire is not pertinent for the substrate for growing GaN films for the purpose of obtaining a freestanding GaN crystal. Recently trials have been done for eliminating sapphire substrates from grown GaN films by a laser. However, the separation of the sapphire substrates from the GaN films is difficult even by high power lasers.
Instead of the sapphire substrate, another candidate which can be eliminated from grown GaN films would be a GaAs substrate. A (111) plane of GaAs has three-fold rotation symmetry. A C-plane GaN film would be grown in vapor phase along c-axis on the (111) GaAs substrate. However, it is found that thick GaN is not grown upon a GaAs substrate. Perhaps differences of lattice constants and thermal expansions between GaAs and GaN cause the difficulty of growing thick GaN on the GaAs substrate. The lattice misfit and the thermal distortion induce large inner stress which forbids a GaN film from growing to a thick crystal. A breakthrough was required for making a thick GaN crystal in vapor phase.
The inventors of the present invention contrived a GaAs-based epitaxial lateral overgrowth method (ELO) for making low-dislocation GaN crystals by preparing a GaAs substrate, making an ELO mask having many small regularly-populated windows on the GaAs substrate, and growing GaN films by a vapor phase growing method on the ELO-masked GaAs substrate. The inventors had filed a series of patent applications based on the GaAs-based ELO methods for making GaN crystal bulks.
{circle over (1)} Japanese Patent Application No.9-298300
{circle over (2)} Japanese Patent Application No. 10-9008
{circle over (3)} Japanese Patent Application No.10-102546
{circle over (1)}, {circle over (2)} and {circle over (3)} have been combined into a PCT application of WO 99/23693.)
{circle over (4)} Japanese Patent Application No.10-171276
{circle over (5)} Japanese Patent Application No.10-183446
An ELO mask is made by preparing a three-fold rotation symmetric GaAs (111) substrate, piling a thin SiN film (e.g., 100 nm thickness) on the GaAs substrate, and forming many small regularly-distributed striped or dotted windows on the SiN film by etching. The round, rectangle or square dotted windows should be arranged at corner points of repeated equilateral triangles forming a six-fold symmetric pattern. The distribution of the windows have hexagonal (six-fold) symmetry. A window has six nearest neighboring windows at sixty degree rotating points on an imaginary circle around the window.
The orientation of the ELO mask is predetermined by equalizing the sides of the basic equilateral triangles parallel to a GaAs[−110] direction or a GaAs[11-2] direction. The SiN mask has a negative function of suppressing GaN growth. The GaAs substrate has a positive function of facilitating GaN growth. At first a thin GaN buffer layer (e.g., 80 nm) is grown on the ELO-masked substrate at a low temperature (500 to 600.degree. C.). At an early stage, GaN nuclei occur only on the exposed substrate in the windows but no GaN nucleus appears on the SiN mask. In this case, the thin buffer layer is formed only on the exposed GaAs substrate parts within the windows. The buffer layer is an assembly of GaN films independently growing from separated GaN nuclei on the GaAs texture.
Then, an epitaxial GaN film is grown in vapor phase at a high temperature. GaN grows further on the buffer layers. Soon the surface of the GaN layer coincides with the mask surface. Then, isolated GaN films enlarge upward within the windows, forming facets following the sides of the windows. Isolated independent facet cones are completed on every windows. Then, conical GaN films change the growing direction from the upward direction to horizontal directions. All the windows generate horizontally preceding GaN film edges in radial directions. Dislocations turn into horizontal directions and accompany the GaN film edges. Since the GaN cones begin to dilate in horizontal directions, dislocation turning points align in slanting planes which coincide with the conical surface of the GaN cones at the time of turning.
Horizontally growing GaN films soon meet with other films growing horizontally from the neighboring windows. There are six identical windows at three points from which GaN films creep on the mask outward at a similar speed. Two opposite GaN films meet on a vertical bisector of a line connecting the windows. Three GaN films meet at a center of an equilateral triangle constructing by the starting windows. The shape of the films creeping from a window is hexagonal at the collision. Since dislocations extend horizontally in parallel with the growing direction, dislocations of antiparallel directions collide with each other. A part of the dislocations is annihilated at the straight collision. Other dislocations again change the direction of extension from horizontal directions to the vertical direction.
After two neighboring GaN films meet on the bisector, the growing direction changes. The GaN films grow in the vertical direction along an c-axis. It is a C-plane growth which maintains the C-plane as a unique, smooth, flat surface. The C-plane growth is a well known-method of GaN growth. A long-term vapor phase growth makes a thick GaN/mask/GaAs samples of several hundreds of thickness. Then, the mask and the GaAs substrate are eliminated by, for example, aqua regia.
The ELO method has an advantage of reducing dislocations by the twice changes of the extending direction of the dislocations. The ELO method enabled the inventors to make a thick (more than about 100 .mu.m) GaN single crystal. The GaN freestanding crystal without a foreign material undersubstrate was produced by the inventors of the present invention for the first time in the world.
However, when the GaN substrate is of low quality, no good devices can be produced on the GaN substrate. Mass production of GaN devices requires good GaN substrates of everywhere low dislocation density.
The epitaxial lateral overgrowth method which makes use of a mask having many windows can produce a GaN crystal of 1.about.2.times.10.sup.7 cm.sup.−2 dislocation density. Reduction of dislocations is insufficient. ELO-made GaN crystals are unsatisfactory as a GaN substrate upon which InGaN type LDs are fabricated. InGaN-LDs require better GaN crystals of far smaller dislocation density.
The inventors of the present invention contrived a new method of reducing dislocations during the growth for making a low dislocation density GaN single crystal of high quality.
{circle over (6)} Japanese Patent Laying Open No.2001-102307 (Japanese Patent Application No.11-273882)
Facet growth was proposed in the document {circle over (6)} by the same inventors as the present invention. All the known GaN growth has been C-plane growth which maintains a smooth, flat C-plane as a surface of c-axis growing GaN. {circle over (6)} denied the conventional C-plane growth and advocated facet growth which makes facets and pits composed of the facets on a growing GaN surface and maintains the facets and pits without burying pits. A GaN facet grows in a direction normal to the facet. Although an average direction of growth is a c-axis direction, microscopic growing directions are non-c-axis directions.
FIG. 1 to FIG. 3 show our previous facet growth. In FIGS. 1(a) and (b), a GaN crystal 2 is growing in a c-axis direction, having a C-plane top surface 7. Crystallographical planes inclining to the C-plane are called facets 6. The facet growth forms facets and maintains the facets without burying facets. In the example of FIG. 1, six facets 6 appear and form a polygonal reverse cone pit 4 on the C-plane surface. The pits built by the facets are hexagonal cones or dodecagonal cones. Hexagonal pits are formed by six-fold rotation symmetric facets of either {11−2m} or {1−10m} (m: integer). Dodecagonal pits are composed of {11−2 m} and {1−10m} (m: integer). Although FIGS. 1(a) and (b) show the hexagonal pit, dodecagonal pits appear prevalently.
To form facet pits, to maintain pits and not to bury pits are the gist of the facet growth. A facet 6 displaces at a direction normal to the facet. A dislocation extends along a growing direction. A dislocation extending along a c-axis and attaining the facet turns an extending direction in a horizontal direction parallel to the facet and reaches a crossing line 8. The crossing lines 8 include many dislocations. As the top surface moves upward, loci of the crossing lines 8 make crossing planes 6 which meet with each other at 60 degrees. Planar defect assemblies 10 are formed on the crossing planes. The planar defect assemblies are a stable state.
Some dislocations attaining to the crossing line turn an extending direction again inward, move inward along the rising slanting crossing line 8 and fall into a manifold point D at a pit bottom. The dislocation substantially runs inward in the horizontal direction. A linear defect assembly 11 is formed along the manifold point D at the bottom of the pit. The linear defect assembly 11 is less stable than the planar defect assemblies 10.
The facets and the pits create the planar defect assemblies and linear defect assemblies by depriving other parts of dislocations. Losing dislocations, other parts are improved to low dislocation density crystals. When the GaN grows to a predetermined thickness, a GaN/GaAs sample is taken out of the furnace. The GaAs substrate and the ELO mask are removed. A freestanding GaN film is obtained. The GaN film can be finished to a smooth substrate by polishing. The GaN film is transparent like a glass substrate. The dislocations cannot be seen by human eyesight. The dislocations are detected by etching the GaN sample by a suitable etchant and observing the etched surface by a microscope. Differences of crystal structures are discernible by cathode luminescence (CL) microscope observation.
The dislocation density of the low dislocation density regions is examined by microscope. The dislocation density there turns out to be as low as 10.sup.6 cm.sup.−2. The former ELO obtained a GaN crystal of dislocation density of 1 to 2.times.10.sup.7 cm.sup.−2. In comparison with the ELO, the facet growth method succeeded in reducing dislocation density down by one order of magnitude. The facet growth was an effective sophisticated method for reducing dislocations.
The inventors noticed that the facet growth method has still problems for producing GaN wafers for making LD chips.
The facet growth can gather dislocations into a narrow volume by making facet pits, growing a GaN crystal without burying facets, gathering dislocations into the bottoms of pits. Dislocations do not necessarily converge to a single point but diffuse outward. When a plurality of 100 .mu.m.phi. pits are formed, dislocations converge to a narrow spot at a bottom of a pit somewhere. But at other regions, dislocations diffuse till about 30 .mu.m.phi. wide range. The 30 .mu.m.phi. diffusion makes a hazy dislocation nebula.
This means that once converged dislocations disperse again to a hazy nebula of dislocation. It was confirmed that lines of the hazy nebulae diffusing from the pit bottom assembly include many dislocations.
If the diameters of pits are increased for enlarging the low dislocation density regions, lines included in the hazy dislocation nebulae increase. Enlargement of pits increases the number of dislocations converged into the pit bottom and the area of the dislocations escaping the bottom and forming hazy nebulae.
Why do once converged dislocations leak and diffuse from the core at the pit bottom? What does release the once core-assembled dislocations from the pit bottom? The inventors of the present invention found that the motivation of release is repulsive forces acting among dislocations. Mutual repulsion is the ground of release of dislocations.
Dislocations extend in the direction of growth, as long as the crystal growth continues. Dislocations sometimes aggregate or segregate. Dislocations do not perish easily by themselves. Dislocations are disorder of lattice structures. When one dislocation comes close to another dislocation, lattice disorder is compressed. Energy of lattices is increased by the approach. The increase of the lattice energy brings about mutual repulsion among dislocations. The repulsion and the lattice dynamics do not appear till the dislocation density is raised at a high value multiplied by 10.sup.3 times or 10.sup.4 times of natural density.
When a thousand dislocations or ten thousand dislocations are converged within a narrow volume, repulsion acting between dislocations increases. Although dislocations are once gathered within a narrow manifold point D at a pit bottom, strong repulsion releases the highly packed assembly of dislocations from the manifold D. Dislocations escaping from the pit bottom make hazy dispersion of dislocation. Occurrence of the nebular hazy dislocation dispersion was a drawback of the previous facet growth.
Hazy dislocation nebulae have very high dislocation density of 10.sup.7 cm.sup.−2 which is ten times as much as an average dislocation density (10.sup.6 cm.sup.−2). Such high dislocation density 10.sup.7 cm.sup.−2 of the hazy dislocation nebulae is insufficient for making use of the GaN crystal as an LD substrate for making LD devices. An LD substrate requires low dislocation density less than 10.sup.6 cm.sup.−2. The occurrence of the hazy dislocation nebulae is the first problem of the previous facet growth.
The second problem is planar defect assemblies which are born by gathering dislocations to the pit bottoms and inclining to each other at 60 degrees. The planar defect assemblies dangle from the crossing lines 8. 60 degrees spacing planar defect assemblies 10 have six-fold rotation symmetry. The planar defect assemblies include high density dislocations. In addition to the hazy dislocation nebulae, the radially extending planar defects assemblies are a serious problem for an LD substrate, since the planar defects would induce degeneration and would restrict lifetime of LDs. An LD substrate requires a reduction of the planar defect assemblies.
The last problem is more fundamental. Occurrence and distribution of pits are stochastic, accidental and unprogrammable. The distribution of pits are entirely at random. The previous facet growth method which reduces dislocations by growing facet pits without burying, has a weak point of undeterminable positions of pits. It is impossible to previously determine or know the spots at which facet pits happen. An accident makes a pit at an undetermined spot. The positions of pits are stochastic variables. The formation of pits are uncontrollable. Accidental formation of pits, stochastic pit positions, stochastic dislocation bundles and random concentration of dislocations are essential feature of the previous facet growth method. Uncontrollability of pit positions is a serious problem.
When many GaN-LD chips were made on the GaN having random pit distribution, it would be probable that an active stripe of an LD overlaps on dislocation bundles. The dislocation bundles in the active layer would accelerate degradation of the laser diodes (LDs) and would shorten the lifetime.
LD chips fabricated on a GaN substrate wafer have various sizes. For example, an LD chip of a 400 .mu.m width and a 600 .mu.m length has an emission stripe of 2 to 3 .mu.m width by 600 .mu.m length. A rate of the (active) emission stripe to the full width of the chip is 3 .mu.m/400 .mu.m. The probability of hazy dislocation nebulae or dislocation bundles overlapping on the stripe is not low. The stripe is as long as a chip length. Hazy dislocation nebulae disperse widely. Planar defects have large sizes. Overlapping of dislocation bundles or hazy dislocation nebulae on an active stripe occurs frequently.
LD producing GaN substrates should enable device makers to avoid active stripes overlapping on dislocation bundles or hazy dislocation nebulae. Such a method which cannot determine the positions at which dislocation bundles happen is inconvenient. For avoiding stripes overlapping on the dislocation bundles, a new method which allows us to control the positions of dislocation bundles positively is ardently desired. The occurrence of dislocation bundles is unavoidable. What is required is a method which can control occurrence and positions of dislocation bundles.
Three matters aforementioned are the problems to be solved by the present invention. In short, the objects of the present invention are converged into three matters;
(1) Reduction of hazy diffusion of dislocations from the defect assemblies of the centers of facet pits.
(2) Annihilation of planar defects occurring at the centers of the facet pits.
(3) Controlling of positions of defect assemblies at the centers of facet pits.
Technical terms are clarified before describing the subject matters of the present invention. Vapor phase growing methods for growing gallium nitride applicable for the present invention include an HVPE method, an MOCVD method, an MOC method and a sublime method. These methods are all inherently used for making very thin films of GaN of about 0.1 .mu.m to 1 .mu.m. The present invention uses these methods for making a very thick bulk crystal of GaN of an order of a 1000 .mu.m thickness. Such a thick crystal is called a GaN “substrate” for discriminating it from a thin film of an order of 1 .mu.m. For avoiding confusion, a starting substrate of a foreign material for growth is often called an “undersubstrate” till now.
1. HVPE (Hydride Vapor Phase Epitaxy) Method
Gallium source is metal gallium (Ga). Nitrogen source is ammonia (NH.sub.3). An HVPE apparatus has a hot-wall furnace, heaters enclosing the furnace, a Ga-boat positioned at a higher spot in the furnace, a susceptor installed at a lower level in the furnace, a vacuum pump and material gas (H.sub.2, NH.sub.3, HCl) supplying tubes. An undersubstrate is put on the susceptor. Metal gallium is supplied into the Ga-boat. The heater heats the Ga-metal into a Ga-melt and the undersubstrate on the susceptor. A mixture gas of hydrogen (H.sub.2) and hydrochloric acid (HCl) is supplied to the heated Ga-boat for synthesizing gallium chloride (GaCl). Gallium chloride (GaCl) is conveyed downward to the undersubstrate on the heated susceptor. Another mixture of hydrogen (H.sub.2) and ammonia (NH.sub.3) is supplied to the heated undersubstrate for making gallium nitride (GaN) by the reaction of GaCl+NH.sub.3.fwdarw.GaN+HCl+H.sub.2. Synthesized GaN is piled upon the undersubstrate for producing a GaN film. The HVPE has an advantage of being immune from carbon contamination, since the Ga-source is metallic gallium (Ga) which includes no carbon and makes GaCl as an intermediate compound.
2. MOCVD (Metallorganic Chemical Vapor Deposition) Method
This is the most popular method for making GaN films on a foreign material (sapphire) substrate at present. Materials of gallium and dopants are organic metals including carbon. Thus, this method is called “metallorganic”. The MOCVD method uses a cold-wall furnace having a susceptor for holding an undersubstrate and a heater for heating the susceptor.
3. MOC (Metallorganic Chloride) Method
The MOC method employs a Ga-including metallorganic compound (e.g., trimethyl gallium) as a Ga material like the MOCVD. The nitrogen material is ammonia (NH.sub.3) gas. Unlike the MOCVD, TMG does not react with ammonia (NH.sub.3). In a hot wall type furnace, TMG reacts with HCl gas for synthesizing GaCl. Vapor GaCl falls toward a heated substrate on a susceptor. The substrate is supplied with ammonia gas. GaCl reacts with ammonia for making GaN. GaN piles upon the substrate and makes a GaN film. The use of the metallorganic compound (TMG) may induce contamination by carbon. However, this method can absorb material gasses higher efficiently than the MOCVD method.
4. Sublimation Method
This method uses no gas as a material. The material of this method is polycrystalline GaN. The solid GaN and a substrate are allocated respectively on places of different temperatures. The solid GaN on higher temperature is heated to vapor and moved to the substrate on lower temperature, so that a GaN film is piled on the substrate.
Orientations of crystals are clarified. Such an elementary matter should belong to a common sense to the skilled in art. But it is not true. Designations of crystal orientations are not well known even to the skilled. There are confusion, misunderstanding and misuse of crystallographical symbols in many academic reports or patent descriptions. The inventors of the present invention are afraid that readers cannot understand space geometric symbols required for describing the present invention. The definition of orientations is now clarified. Unlike sapphire (trigonal symmetry), gallium nitride (GaN) belongs to hexagonal symmetry (a=b=d.noteq.c, .alpha.=.beta.=.delta.=120.degree., .gamma.=90.degree.). Three axes, a-axis, b-axis and d-axis, extend in three directions with 120 degrees rotation on the xy-plane. The c-axis is orthogonal to the a-, b-, d-axes. Three index representation and four index representation type have been used for designating hexagonal symmetry structure. Here, the four index representation is employed for describing the present invention. Rules of the four-index representation are preliminarily described.
Rules have been determined for the representation of crystallographic planes and directions. There are collective representation and individual representation both for a plane and a direction. Collective representation of planes is wavy-bracketed four Miller indices {hkmn}. Here, h, k, m and n are integers called Miller indices (or plane indices) which are used in common for representing both planes and directions. Individual representation of directions is round-bracketed four Miller indices (hkmn). Collective representation of directions is key-bracketed four Miller indices <hkmn>. Individual representation of planes is rectangular-bracketed four Miller indices [hkmn]. An individual direction [hkmn] is perpendicular to an individual plane (hkmn) having the same Miller indices.
Allowable symmetry operations are determined by the symmetry group to which the crystal belongs. Even hexagonal symmetry includes several different symmetry groups. If a plane or a direction is converted to another plane or direction by the allowable symmetry operations, the two planes or directions are represented by a common collective representation. GaN has three-fold rotation symmetry which allows cyclic commutations of three indices khm.fwdarw.hmk.fwdarw.mkh.fwdarw.khm. However, the c-axis index “n” is a unique one which cannot be exchange with three other indices k, h and m. Collective plane representation {hkmn} includes all the individual planes to which an individual plane (hkmn) can attain by the allowable symmetry operations. As mentioned before, hexagonal symmetry still has variations with regard to the allowable symmetry operations.
The above fate is restricted to GaN which has three-fold rotation symmetry. Rigorously speaking, (hkmn) is not identical to (khmn) in GaN which lacks six-fold rotation symmetry and inversion symmetry. But it is promised here that a collective representation {hkmn} includes six different individual representations (hkmn), (kmhn), (mhkn), (hmkn), (khmn) and (mkhn). Collective representations {hkmn}, {kmhn}, {mhkn}, {hmkn}, {khmn} and {mkhn} are all an identical representation. Miller indices are negative or positive integers. Negativity should be designated by an upperline by crystallography. However, patent description forbids upperlines. Then, negativity is denoted here by affixing “−” sign before an integer. The above rules are also applicable to the representations of directions <hkmn> or [hkmn].
Hexagonal GaN has three identical axes which can be converted by three-fold rotations. Two of the three are called a-axis and b-axis. Third axis has no name. The third axis is here named d-axis for alleviating inconvenience. Namely, a-axis, b-axis and d-axis are defined with a 120 degree angular spacing on a horizontal plane. The three are equivalent axes. A unique axis perpendicular to the three axes is a c-axis. Crystal planes (hkmn) are a set of an indefinitely large number of parallel planes with a definite spacing which are imagined in an indefinitely large crystal. Miller indices are defined by inverse numbers of the lengths of segments at which a first plane crosses the four axes. When the first plane crosses a-axis at a/n, b-axis at b/k, d-axis at d/m and c-axis at c/n, the set of planes is designated by Miller indices (hkmn).
A plane with smaller plane indices is a more fundamental plane having smaller numbers of equivalent planes. An individual orientation [hkmn] is defined as a direction which is perpendicular to an individual (hkmn) plane. Three forward indices k, h and m are not independent. The freedom allocated to the three indices is two. Two-dimensional directions and planes on xy-plane can be denoted by two independent parameters. Thus, an alternative representation indicates two dimensional orientations with two indices. However, this description employs the four index representation hkmn which uses three indices k, h and m for designating two dimension orientations and planes for the sake of simplicity of symmetry. In the four index representation, three forward indices always satisfy a sum rule h+k+m=0.
GaN has three primary planes. One is C-plane which is represented by (0001). C-plane is a plane which is vertical to c-axis. Corresponding plane and axis are perpendicular to each other. Don't confuse planes with axes. For clearly discerning planes from axes, planes are denoted by capital letters and axes are denoted by small letters. A GaN crystal has three-fold symmetry around c-axis. Namely, it is invariant for a 120 degree rotation by c-axis. When a GaN film is grown heteroepitaxially upon a substrate of a foreign material, e.g., GaAs or sapphire, only a c-axis growth occurs. GaN lacks inversion symmetry. (0001) plane is different from (000−1) plane. C-plane satisfies the sum rule h+k+m=0+0+0=0.
Another typical plane is M-plane which is a cleavage plane. M-plane crosses one axis of three symmetric axes at a positive unit edge, crosses another axis at a negative unit edge and is parallel with the last symmetric axis and c-axis. M-plane is indicated by collective representations {1−100}, {01−10}, {−1010}, {−1100}, {0−110} and {10−10} which are all equivalent and denote the same set of six planes. M-plane is otherwise indicated by individual representations (1−100), (01−10), (−1010), (−1100), (0−110) and (10−10) which denote different individual planes belonging to M-plane. Each of the collective representations { . . . } indicates an equivalent set of six planes. But the individual representations ( . . . ) designate different planes. M-plane satisfies the sum rule h+k+m=1+(−1)+0=0. Individual planes cross each other at 60 degrees. M-plane is a convenient nickname of {1−100}, {01−10}, {−1010}, {−1100}, {0−110} or {10−10} planes. M-plane is important planes.
Third typical plane is A-plane. A-plane crosses two axis of three symmetric axes at positive unit edges, crosses the last axis at a negative half of unit, and is parallel with c-axis. A-plane is indicated by collective representations {2−1−10}, {−12−10}, {−1−120}, {−2110}, {1−210} and {11−20 } which are all equivalent and denote the same set of six planes. A-plane is otherwise indicated by individual representations (2−1−10), (−12−10), (−1−120), (−2110), (1−210) and (11−20) which denote different individual planes belonging to M-plane. Each of the collective representations indicates an equivalent set of six planes. But the individual representations designate different planes. Individual planes cross each other at 60 degrees. A-plane satisfies the sum rule h+k+m=2+(−1)+(−1)=0.
GaN crystal lacks six-fold rotation symmetry. All the six individual planes are different planes in the category of A-plane. The individual planes meet each other at 60 degrees. A-plane is also a nickname. <2−1−10> direction is perpendicular to (2−1−10), one of A-planes. <2−1−10> direction is parallel with one of M-planes. Although (2−1−10) is called an A-plane. <2−1−10> is not called “a-direction”. Similarly, <1−100> direction is perpendicular to (1−100), one of M-planes and parallel to one of A-planes. C-plane, A-plane and M-plane are primary, typical, significant planes in GaN crystals. One of A-planes, one of M-planes and C-plane are orthogonal to each other. Thus, one of A-planes, one of M-planes and C-plane can form a three dimensional orthogonal coordinate system.
A “facet” is another important concept for describing the technical idea of the present invention. A facet is a crystallographical plane (hkmn) which can be also represented by low Miller indices h, k, m and n. But, facets are not the aforementioned typical planes A, M and C. Facets have different indices from three primary planes. Some facets have indices resembling the primary planes A, M and C. {2−1−11} and {2−1−12} are facets deriving from A-plane. {1−101} and {1−102} are facets originating from M-plane. Equivalent six facets built a hexagonal conical pit. A hexagonal pit consists of A-plane-derivative {2−1−11} facets or {2−1−12} facets. Another hexagonal pit constructed by M-plane-derivative {1−101} facets and {1−102} facets. Sometimes dodecagonal conical pits are formed. An assembly of the six A-plane-derivative {2−1−11} or {2−1−12} facets and six M-plane-derivative {1−101} or {1−102} facets form dodecagonal cone pits. Further, sometimes double stepped dodecagonal pits appear. An upper dodecagonal reverse-cone comprises lower n facets {2−1−11} and {1−101} which have steeper inclinations. A lower dodecagonal reverse-cone comprises higher n facets {2−1−12} and {1−102} which have smaller inclinations.
The fourth index “n” takes 1 or 2 in the above facets. In many cases, facets having low indices appear on GaN surfaces in practice. High indices facets do not appear so frequently. For example, if A-planes {2−1−10} are inclined to c-axis by a small angle, {2−1−11 } facets are obtained. If {2−1−11} facets are further inclined to c-axis by an additional small angle, {2−1−12} facets are obtained. They are A-plane-derivatives. A bigger fourth index n means a bigger pitch angle to c-axis and a smaller inclination to the horizontal plane. The fourth index “n” takes n=1 or n=2 for many facets. Higher than 3 of index n is exceptional for practical facets.
Concepts of double stepped facets or double stepped pits are clarified. Steeper facets or steeper pits are upper facets or pits having smaller n. A steeper facet pit appears on upper part of a double stepped pit. Milder facets or milder pits are lower facets or pits having larger n. A milder facet pit appears on lower part of a double stepped pit.
Most of the facets appearing at pits are A-derivative {11−22} and M-derivative {1−101 } facets. A length of a-axis is denoted by “a”. Another length of c-axis is denoted by “c”. An inclination angle of {1−101} facet to c-axis is tan.sup.−1(3.sup.1/2a/2c). Another inclination angle of {11−22} facet to c-axis is tan.sup.−1(a/c).
Shallower, milder facets are, for example, {11−23}, {1−102}, {11−24}, {1−103} which have a large index n. An inclination angle of {1−10n}(n.gtoreq.2) facet to c-axis is, in general, tan.sup.−1(3.sup.1/2a/2cn). A smaller inclination angle is given by a bigger n. Another inclination angle of {11−2n}(n.gtoreq.3) facet to c-axis is, in general, tan.sup.−1(2a/cn). A smaller inclination angle is given by a bigger n. Thus, a facet of higher n is a milder, shallower facet.
GaN crystal is a wurtzite(ZnS) structure belonging to the hexagonal symmetry group. An equilateral hexagonal column includes a hexagonal bottom plane having six Ga atoms at six comers and a Ga atom at the center, a ⅜ unit height intermediate plane having six N atoms at six comers and a N atom at the center, a ½ unit height intermediate plane having three Ga atoms at centers of three sub-triangles, a ⅞ unit height intermediate plane having three N atoms at centers of three sub-triangles which are just above the Ga atoms on the ½ plane, a top plane having six Ga atoms at six corners and a Ga atom at the center. A hexagonal symmetric column (6Ga+6N) has three unit cells which include two Ga atom and two N atoms. A GaN crystal has three-fold rotation symmetry. But, the GaN crystal lacks inversion symmetry and six-fold rotation symmetry.
Suitable undersubstrates for growing the GaN crystal are sapphire(.alpha.−Al.sub.2O.sub.3), silicon (Si), or gallium arsenide (GaAs) etc. Sapphire has not hexagonal symmetry but trigonal symmetry. Symmetry is poor. Sapphire lacks three-fold rotation symmetry and inversion symmetry. Poor symmetry deprives sapphire of cleavage.
Silicon (Si) does not have hexagonal symmetry but has cubic symmetry which requires three Miller indices (khm). Si takes the diamond structure. The three Miller indices have no sum rule. Thus, k+h+m.phi. in general. A three-fold rotation symmetric axis is a <111> direction of an orthogonal line. A three-fold rotation symmetric plane is described as (111). Ordinary Si devices are fabricated on a (001) Si wafer for making use of the natural cleavage. Since (001) plane lacks three-fold rotation symmetry, a (111) Si can be a candidate as a substrate for growing hexagonal GaN.
A Gallium arsenide (GaAs) crystal has not hexagonal symmetry but cubic symmetry. GaAs takes zinc blende (ZnS) structure. Miller indices are three. A three-fold rotation symmetric axis is a <111> direction of an orthogonal line. A three-fold rotation symmetric plane is described as a (111) plane. Ordinary GaAs devices are made upon a (001) GaAs wafer for making use of natural cleavage {1−10} perpendicular to surfaces. GaN growth requires three-fold rotation symmetry. Thus, a three-fold symmetric GaAs (111) wafer should be employed. GaAs lacks inversion symmetry. Thus, (111) planes and (−1−1−1) planes are not equivalent. One of {111} planes is Ga atoms overall aligning surface. The other {111} plane is As atoms overall aligning surface. The former is designated by a (111) Ga plane. The latter is designated by a (111)As plane.
Denying the prevalent C-plane growth, the former GaN facet growing method contrived by the present inventors was an excellent method for growing a low dislocation GaN film by maintaining the facet growth without burying facets, gathering dislocations to pit bottoms and reducing dislocations in extra portions except the pit bottoms. As described till now in detail, the previous GaN facet growth method has still three problems which should be solved.
(1) To reduce hazy dispersion of dislocations diffusing from defect assemblies at pit bottoms (FIG. 3(2)),
(2) To annihilate planar defect assemblies following facet boundaries (FIG. 1(b)),
(3) To control positions of defect assemblies formed below facet pit centers.
All the three are difficult problems. Difficulties are again clarified here. The serious problem of the previous facet growth of the inventors which maintains facets and pits without burying the facets was an unstable state of defect assemblies at pit bottoms. FIGS. 3(1) and (2) show the states of defect assemblies of our previous facet growth method. Accidentally a pit 14 with facets 16 occurs somewhere on a growing GaN film surface. The positions of the pits cannot be determined previously. Occurrence of pits and points of occurrence of pits fully depended on contingency. Occurrence of pits and positions of pits were uncontrollable. In accordance with the GaN growth in an upward direction, facets 16 rise and dislocations move in the horizontal direction to the center of the pit 14. A dislocation bundle 15 is formed at the bottom of the pit 14. As shown in FIG. 3(2), the dislocation bundle is neither encapsulated nor arrested by anything. Ephemerally assembling, individual dislocations in the dislocation bundle have a strong tendency of diffusing and dispersing outward again by mutually acting repulsive force.
The facet growth gathers plenty of dislocations to the center bottoms of facet pits by making use of the anisotropy of the movements of dislocation on the facets. One problem is the dislocation-assembled state at the pit bottoms. The anisotropic sweeping function of the facet pits can gather dislocations to the pit bottoms. But, the fact pits have no function of perishing dislocations. Besides, the pits are open. The pit-dangling dislocation assemblies are not closed. Dislocations survive. Total number of dislocations is not reduced.
Excess high concentration of dislocations gives the dislocation assemblies the tendency of releasing and relaxing dislocations outward. The tendency incurs difficult problems.
When two dislocations having plus and minus Burgers vectors collide, the two dislocations will perish by cancellation. However, the dislocations occurring in the same facet should have Burgers vectors of a common sign with high probability. Collision of two dislocations having common sign Verger's vectors has no power of annihilating two dislocations. Dislocations of common Burgers vectors survive the collision. Without extinction, dislocations are converged to the open pit bottoms for making planar defect assemblies and linear defect assemblies as shown in FIG. 1(b), FIG. 2 and FIG. 3.
Assembling of dislocations of common sign Burgers vectors into planar defect assemblies and linear defect assemblies is not permanent but transient. Dislocations diffuse from the assemblies to hazy dispersion. Hazy dispersion raises the dislocation density of the regions around the defect assemblies again. What induces such a hazy distribution of dislocations? Why do dislocations diffuse as haze? The inventors of the present invention think that the motivation of the dislocation diffusion would be the repulsive forces acting between two dislocations having same sign Burgers vectors.
Dislocations are displacements of lattices. If dislocations having the same sign Burgers vectors are converged at a point, the displacements are enhanced, which raises the lattice dynamic energy. Repulsive forces are caused by the convergence of the same sign Burgers vector dislocations for reducing dynamical energy. Strong repulsion acts the aggregate of dislocations, releases the dislocations from the aggregate and makes a hazy dispersion of dislocations. FIG. 3(2) shows the release of once aggregated dislocations from the central dislocation bundle. It is a regrettable fact for the prior contrivance that once-converged dislocations again diffuse outward by the strong repulsion into hazy dislocation distribution.
Mergers of pits perturb dislocation bundles. Unification of dislocation bundles concentrates dislocations. Enhancement of dislocation density widens the hazy dispersion of dislocations. This is the aforementioned problem (1) of the hazy dislocation dispersion.
When dislocations are swept into the facet pit centers, 60 degree rotating planar defect assemblies are sometimes generated under the pit bottom center. The planar defect assemblies 10 are shown in FIG. 1(b). Hanging from the boundaries, the defects assemble into 60 degree rotating planes. The same sign dislocations cannot fully converge to a central point due to the strong repulsion. Then, the planar defect assemblies 10 are built below the bottom of the pit. The repulsion stabilizes the diffused planar defect assemblies 10.
When a plurality of facet pits merge into a big pit, the number of the dislocations which converge to the pit center is also increased and large planar defect assemblies are produced.
The positions at which the facets appear are accidental and irregular, since the facet pits are born at random by natural phenomenon for reducing free energy. The positions of the pits are uncontrollable. The pit positions are irregular, unpredeterminable and random. The relaxed hazy dislocation bundles is an obstacle of making devices on the GaN substrate which has been made by the previous method. An increase of the area of hazy dislocation bundles lowers the quality of devices and decreases the yield of making devices.
A serious problem of the previous contrivance is that the dislocations once gathered to the centers of the facet pits are not permanently captured but are soon released from the bottoms of the facet pits (relaxing bundles 15 in FIG. 3(2)).
The inventors of the present invention think that if the dislocation aggregate would have a dislocation annihilation/accumulation mechanism which arrests dislocation everlastingly, the diffusion and the release of dislocations would not occur. The dislocation annihilation/accumulation mechanism would be very useful.
The dislocation annihilation/accumulation mechanism can annihilate and capture many dislocations in a narrow, restricted region. The dislocation annihilation/accumulation mechanism would prevent dislocations from releasing outward or making planar defect assemblies.
What is the dislocation annihilation/accumulation mechanism? What can be utilized as a dislocation annihilation/accumulation mechanism? The present invention intentionally produces crystal boundaries and makes the best use of the boundaries for manufacturing low dislocation density GaN single crystals. FIG. 4 shows the action of the facets, pits and grain boundary of reducing dislocations. A growing GaN crystal 22 has a pit 24 consisting of facets 26. The facet pit 24 is not buried but maintained during the GaN growth. Top of the crystal is a C-plane surface 27. The facet pit 24 has a central bottom 29. When the GaN film further grows, facets 26 grow in the direction vertical to the facets 26. Dislocations are swept in the centripetal, horizontal directions to the pit center. The directions of dislocations are parallel to the C-plane 27. The dislocations attracted to the center are affiliated to dislocation assembly 25 at the pit bottoms 29. The dislocation assembly 25 is encapsulated by boundaries (K) 30. The dislocation assembly is called a “closed defect accumulating region (H)”, since the region arrests, accumulates and is closed by the boundary (K). The closed defect accumulating regions (H) 25 have a very significant function of attracting, absorbing, annihilating and accumulating dislocations permanently.
Once dislocations are arrested, the dislocations cannot escape from the closed defect accumulating regions (H). Thus, the region (H) is “closed”. What closes the region (H) is the grain boundary (K).
The next problem is how to make a grain boundary K encapsulating the closed defect accumulating region (H). The fact that the facet growth which maintains facets without burying facets has the power of gathering the dislocations to the bottoms of the facet pits has been already described. The boundary (K) can be produced by making a crystal different from the surrounding single crystal parts at the bottom centers of the pits. The difference between the central crystal (core) and the surrounding single crystal parts makes an interface boundary. Various differences are allowed for the core crystal enclosed by the boundary, since the surrounding single crystals have a definite predetermined orientation. The central core may be a single crystal of an entirely different orientation from the surroundings, a single crystal of an orientation slightly inclining to the surroundings, a single crystal of an antiparallel c-axis <0001>to the surrounding region orientation, or a polycrystal having not a uniquely-defined orientation. In any case, the boundary K is produced between the core crystal and the surroundings. First, the polycrystalline core is clarified.
In the concrete, a polycrystalline region is formed at the center of a pit. The crystal boundary K is made between the surrounding single crystal regions and the narrow polycrystal region below the pit center. The present invention exploits the boundary K as a dislocation annihilation/accumulation region. The boundary solely or the boundary and the polycrystalline core cooperatively annihilate and accumulate dislocations. For the purpose of decreasing the dislocations, the present invention positively creates a dislocation-full boundary K for annihilating and accumulating the dislocations. It is a surprising, novel idea.
The formation of a sink (absorber; K) of dislocations enables the present invention to prevent hazy dislocation distribution from dispersing further and planar defects at the pit centers from diffusing outward. The sink absorbs and annihilates dislocations.
A pile of search has taught the inventors that some other regions besides a boundary of a bottom-following polycrystal region can act as a dislocation annihilation/accumulation region. A single crystal region following the pit bottom can prepare a dislocation annihilation/accumulation region, so long as the orientation of the bottom-following single crystal has an orientation different from the surrounding single crystal portions. The difference of the orientations produces a boundary (K) between the bottom-following single crystal region and the surrounding single crystal portions. The boundary (K) can be assigned as a dislocation annihilation/accumulation region. For example, a bottom-following single crystal having a reverse <0001> axis can make an interface boundary (K) as a dislocation annihilation/accumulation region.
Furthermore, even a bottom-following single crystal having the same orientation as the surrounding single crystal portions can be a candidate for preparing a dislocation annihilation/accumulation region, so long as the bottom-following single crystal is enclosed by a planar defect assembly or a small angle boundary. The encapsulating planar defect assembly or the small angle boundary acts as a dislocation annihilation/accumulation region.
If a pit bottom following region is one of the following;
A. polycrystal region,
B. single crystal region having a unique orientation different from that of the surrounding single crystal portions,
C. single crystal region having a common orientation with that of the surrounding single crystal portions but being encapsulated by a small angle boundary,
a boundary (K) is generated between the bottom-following region and the surrounding single crystal portions, and the boundary (K) can be a dislocation annihilation/accumulation region. The a dislocation annihilation/accumulation region is effective for lowering dislocation density. The inner region for producing a boundary contains high density defects. The inner region is enclosed by the boundary. Then, the inner region is a closed part accommodating many dislocations. The inner region is named a “closed defect accumulating region (H)”. This is a novel structure.
The closed defect accumulating region (H) means a region which is formed just below a bottom of a facet pit by the facet growth and is composed of a core (S) having a different crystal from the surrounding single crystal portions and a crystal boundary (K) enclosing the core (S). Namely, a closed defect accumulating region (H) consists of a core (S) and a boundary (K). The core (S) is one of polycrystal A, slanting single crystal B and small-angle-boundary-enclosed single crystal C. Symbolically speaking,H=S+K. 
K=A, B or C.
The boundary (K) can annihilate and accumulate dislocations. Dislocation annihilation power is a novel function of the boundary (K). Permanent confinement of dislocations is another important function of the boundary (K). Encapsulation of the core (S) is another function of the boundary (K). A core (S) is formed at a bottom of a facet pit. The core (S) is either a polycrystal or a single crystal. The core (S) is enclosed by the boundary (K). The core (S) sometimes has a function of the dislocation annihilation/accumulation region. A sum of the boundary (K) and the core (S) is a closed defect accumulating region (H). The boundary (K) and some kinds of the core have the function of the dislocation annihilation/accumulation.
The above-cited {circle over (6)} Japanese Patent Laying Open No.2001-102307 was unable to predetermine positions of the pits on a surface. The positions of the closed defect accumulating regions (H) which hang from the bottoms of the pits were undeterminable in the method. {circle over (6)} has still a significance of clarifying the tight relation between the pit bottoms and the closed defect accumulating regions (H). The inventors of the present invention wished to determine the positions of pits. The inventors have hit on an idea of predetermining the positions of the pits. The present invention derives from the idea.
If the positions of the closed defect accumulating regions (H) can be determined by some means, the positions of the pits are also determined indirectly by the same means.
The contrivance of determining the positions of the closed defect accumulating regions (H) will be described later in detail. By short, the positions of the closed defect accumulating regions (H) can be definitely determined by implanting seeds at desired positions. The seeds should have a function of delaying the growth of GaN. The seeds will produce pits which yield the closed defect accumulating regions (H).
If a closed defect accumulating region (H) is made at a predetermined spot, a small cavity is formed at the same spot, since the growing speed at the closed defect accumulating regions (H) is slower than that in the other regions of the C-plane growth. Once the small cavity is formed, an inner conical wall is composed of stable facets of low Miller indices. Crystal growth enlarges the cavity to a pit. The pits survive the whole crystal growth, rising upward. The pits produce the closed defect accumulating regions (H) just at the bottoms. Since the pits and the bottoms rise, the hanging closed defect accumulating regions (H) grow in the vertical direction. Thus, the positions of the closed defect accumulating regions (H) become a controllable factor. Probability of producing the closed defect accumulating regions (H) at arbitrary points is one of the important features of the present invention.
There is another mode of making a closed defect accumulating region (H) beside the aforementioned case. A pit is composed of a set of facets. Sometimes the facets are formed in two steps. FIG. 5(B) shows the two step pit. Upper larger, steeper facets and lower smaller, milder facets coexist in a pit. The milder, shallower facets fix the position of the pit bottom. The shallower facets form upper interface of the following closed defect accumulating region (H).
There are several motives of forming the closed defect accumulating regions (H). When a polycrystal is once generated upon a seed, a polycrystalline closed defect accumulating region (H) is made. The polycrystalline closed defect accumulating region (H) is clearly discriminated from the surrounding single crystal regions. The single/poly interface is the boundary (K).
The closed defect accumulating regions (H) are sometimes single crystals. Single crystalline closed defect accumulating regions (H) have orientations different from the surrounding single crystal regions. Difference of orientations varies further. Why the orientations of the closed defect accumulating regions (H) vary? The facet pits make lower, smaller, milder facets with lager index n. The lower facets which compose a part of the following closed defect accumulating region (H) determine the orientation of the following closed defect accumulating region (H). Then, single crystalline closed defect accumulating regions (H) differ from the surrounding single crystal regions in orientations. The difference of the orientations forces to make the boundary (K). The boundary (K) encloses the core (S). Thus, the inner region within the boundary (K) becomes a “closed” defect accumulating region (H).
The present invention succeeds in solving three above-mentioned problems by producing the closed defect accumulating regions (H) where H=S+K. The hazy dislocation diffusion is completely forbidden, since the dislocations are annihilated/accumulated in the boundaries (K) or both the boundary (K) and cores (S) of the closed defect accumulating regions (H). 60 degree rotation symmetric planar defects at the bottom are extinguished, since the dislocations are annihilated/accumulated in the boundaries (K) or both the boundaries (K) and cores (S). The positions of the closed defect accumulating regions (H) are definitely determined by the seeds.
The present invention solves the problem of uncertainty of the pit positions which would allow LD active stripes to overlap pits by predetermining the pit positions by regular, periodic seed implantation. Programmable pit positions are an advantage of the present invention.
The principles founding the present invention have been described.